Arc tangent to line and arc

[AllenJessup]

I thought this would be simple but I can't get it to work.

I'm trying to draw an arc that's tangent to a line at a specific point and tangent to an arc. I drew the line, started the arc command, hit enter to force the arc tangent to the line at the endpont and then tried to use a Tangent OSnap to hit tangent to the arc. This is what I got. Note the Tangent snap at the midpoint of the arc.

If I accept the Tangent snap it does draw the new arc to the midpoint of the existing arc. Definitely not tangent.  Does this mean there is no solution? I think I'm missing something. I'm usually aiming for a set radius and have no trouble. This is kind of a Best Fit situation. The only criteria are that the new arc be tangent to the red line at the intersection with the yellow line and tangent to the red arc.

Allen

[HorizontalCurveGuy]

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@AllenJessup wrote:

OK. The Lisp comes out with the same answer as the formula,16.4048. However I'm still missing tangency to the arc by 0.05783658m. The tangency on the line is perfect. I'm going to start a gain and see if I can figure why I'm seeing that.

For some reason I've been having trouble with arcs in this drawing. I have a SR open with Autodesk regarding fillet results that don't quite fit.

Allen

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16.4048 is the answer to the equation if the angle used is 121 degrees, but the angel is not 121 Use these numbers and you will get :

Trust me, its correct. And I believe Doni's lisp is using the formula.

16.268449m

Point of tangency coordinate accurate to 5 decimal places.

[AllenJessup]

OK. I probably caused a lot of confusion when I posted the drawing. I later found that while the yellow line was still perpendicular to the red line. It had been moved aprox. 0.10 away. So there were 2 endpoints there and close to each other. This is what I actually needed to work with:

So the final answer is 16.40508700.

I still havn't been able to do it with an Alignment because my alignment tools won't work. I'll tackle that tomorrow.

Allen

[jefflambert9091 · Accepted solution]

I was excited to see this problem. Have used this test problem with our new surveyors.

I just skimmed through the posts and if a solution was given, I apologize.

I like basic cad.

Take a line 90 degrees to your tangent, copy it to the radius of the curve you want to hit, extend the line to the curve, draw a line from that intersection to the end tangent. Now extend the curve to hit it. That is the PRC. Extend it to the original line at 90 degrees to your tangent and you have your radius.  

[Pointdump]

Jeff,

Are you any kin to Johann Heinrich Lambert, inventor of the Transverse Mercator and Lambert Conformal Conic Map Projections?

Dave

[Pointdump]

Allen,

See what you started? This Monster Thread might soon dwarf the "2015 Bug List" thread. 

P.S. I was having problems with my Alignment Tools, too, until Joe squared me away.

Dave

[Neilw_05]

I tested your geometry and I don't get a solution. Please review the screen recording and see if I followed the steps properly.

http://screencast.com/t/zy5VGQJpL

[Neilw_05]

I've found the missing piece to your graphical solution Jeff. The center of the final arc is found by projecting the perpendicular bisector of the chord between the original tangent line and the PRC. See screen recording.

http://screencast.com/t/rbP7Ttgq

One kudo for you. Well done!

[HorizontalCurveGuy]

Excellent!

[doni49]

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@Neilw wrote:

I've found the missing piece to your graphical solution Jeff. The center of the final arc is found by projecting the perpendicular bisector of the chord between the original tangent line and the PRC. See screen recording.

http://screencast.com/t/rbP7Ttgq

One kudo for you. Well done!

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I must be missing something.  How did you find the end point of the chord line (the point shown in the image)?

EDIT:  Never mind.  I took another look and realized you're offsetting through the center pt of the original curve the perpendicular line that was drawn at the end of the tangent line.  Nice!  I love the way this board comes together to help everyone.  🙂

[AllenJessup]

That's wonderful Jeff. I was hoping for a graphical solution. I had a feeling that there must be one. In fact if there is a mathematical solution I think there has to be a graphical proof.

Now I have to ask the inconvenient question. Why won't the software do it? Why does the tangent snap take you to the middle of the arc? This is the type of thing AutoCAD should excel at!

Allen

[AllenJessup]

Don,

Copy the line drawn at 90° to the original tangent line to the center of the arc. Then extend that line to intersect the arc. That intersection gives you that point.

Allen

[doni49]

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@AllenJessup wrote:

Why won't the software do it?

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My guess would be a software bug.  I can't imagine that they'd ever intentionally plan for it to do what you've experienced.

[Joe-Bouza]

It does it for me. accurate to 8 decimal places

[AllenJessup]

What does it Joe?

Don's Lisp does it right down to 14 decimal places. Strangely the graphical solution fails after 11 places.

Allen

[doni49]

Allen,

I set my units to the maximum precision it allows me to do:  8 decimal places.  How are you finding that the measurement is off at 11 decimal places?

[jefflambert9091]

8, 11, or 14 decimal places… I’ll take it!

After drafting thousands of lots is subdivision in the old days, plain AutoCAD was about it. I have just been used to using plain CAD for this purpose. The fillet command works well!! I tried the software and after a while I just gave up. I am now inspired to find out why the software won’t do it.  

Dave, I don’t think I am related to Johann. Maybe, if I was I might have learned about it a little quicker! I have always wondered! 🙂

Thanks for all the positive feedback!

[AllenJessup]

Don,

Draw a line from endpoint to endpoint and used this lisp to list the length of that line to 14 decimal places.

AutoCAD will tell you you've drawn a zero length line but don't believe it.

Allen

;; Return line length to 14 decimal places as a string.
:: By Joe Burke in Autocad 2006 discussion group on 02-09-2006

(defun c:LG ( / e )
  (vl-load-com)
  (if (setq e (car (entsel "\nSelect line: ")))
    (progn
      (setq e (vlax-ename->vla-object e))
      (rtos (vlax-get e 'Length) 2 14)
    )
  )
)
(princ "Type LG to start") ;end

[doni49]

ok.  I was trying to measure with plain old acad tools.  When I use autolisp to measure, it shows me what you're talking about.

When I used my lsp routine, and then do as you say, it produces a line that's "0.00000000001029" long.  When I use the graphical solution, I get a line that's "0.00000000000575".  So in my test case, the graphical solution was actually more accurate than the lisp routine version.

[AllenJessup]

I've posted a Screencast of this answer https://screencast.autodesk.com/Main/Details/01a2eca4-27cc-40e4-9691-1f606c3a741b

Thanks very much, Jeff, for helping me with some of the basic AutoCAD skills I've lost over the years.

Allen

[AllenJessup]

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doni49 wrote:

When I used my lsp routine, and then do as you say, it produces a line that's "0.00000000001029" long.  When I use the graphical solution, I get a line that's "0.00000000000575".  So in my test case, the graphical solution was actually more accurate than the lisp routine version.

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That's strange. Every time I use your Lisp I get zeros out to 14 places. Are you using Fillet to trim out the circle?

Allen